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A new hyperspectral endmember detection method that represents endmembers as distributions, autonomously partitions the input data set into several convex regions, and simultaneously determines endmember distributions (EDs) and proportion values for each convex region is presented. Spectral unmixing methods that treat endmembers as distributions or hyperspectral images as piecewise convex data sets have not been previously developed. Piecewise convex endmember (PCE) detection can be viewed in two parts. The first part, the ED detection algorithm, estimates a distribution for each endmember rather than estimating a single spectrum. By using EDs, PCE can incorporate an endmember's inherent spectral variation and the variation due to changing environmental conditions. ED uses a new sparsity-promoting polynomial prior while estimating abundance values. The second part of PCE partitions the …